There were no details immediately available about the arrest.
"We are aware of the situation involving William Moore and are in the process of gathering more information," the team said in a statement. "Because this is now a legal matter, the club will have no further comment at this time."
Moore started 12 games for the Falcons last season, but missed the final four weeks of the regular season while resting a hamstring injury. The fifth-year veteran was a Pro Bowl alternate in 2012 and ended up playing in the NFL's annual All-Star game because 49ers safeties Donte Whitner and Dashon Goldson played in the Super Bowl.
The Falcons signed Moore to a five-year, $30 million deal in March that included $14 million in guaranteed money.
Moore has been in Atlanta since 2009 when the Falcons made him their second-round pick in the NFL Draft.
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